Sam Evens, Math 60210, Basic Graduate Algebra I, Fall 2023
HH 117, 2-3:15
Office hours: TBA, or after class, or by appointment. You can arrange a meeting either by talking to me or by emailing me at sevens (at sign) nd (dot) edu to arrange a meeting.
Robert Ash, Abstract Algebra: The Basic Graduate Year. This is available from Dover, but there are copies available on the web.
Serge Lang, Algebra, Revised 3rd edition, Springer-Verlag.
Michael Artin, Algebra , Prentice Hall.
D. Dummit and R. Foote, Abstract Algebra, Prentice Hall.
Serre, Groupes Finis, course notes used for proofs of Sylow theorems
Notes by A. Myasnikov on free groups provides more detail than Ash, V.5.8
8-31 Lecture Notes, Lagrange's theorem
9-12 Lecture Notes on Products
9-14 Lecture Notes on Group Actions
9-19 Lecture Notes: orbit-stabilizer
9-21/9-26 Notes, Sylow theorems
9-28 Lecture notes, applications of Sylow theorems
10-5 Lecture Notes, solvable and nilpotent groups
10-10 Lecture Notes, free groups
10-24 Ring homomorphisms and ideals
10-26 isomorphism theorems and products
10-31 lecture on maximal and prime ideals
11-9 Notes on 2.7, Euclidean domains
11-30 Notes on 4.3, direct sums and bases
12-5, part 1, mostly on direct sums
12-7, classification of finitely generated modules over a PID
Problem Set 1, do at least 7 problems due Tuesday August 29
Problem Set 2 due Tuesday September 5
Problem Set 3 due Tuesday September 12
Problem Set 4 due Tuesday September 19
Problem Set 5, due Tuesday, 9-26
Problem Set 6 due Tuesday 10-10
Problem Set 7 due Tuesday 10-24
Problem Set 8 due Tuesday 10-31
Problem Set 9 due Tuesday November 7
Problem Set 10 due Tuesday November 14
Problem Set 11 due Tuesday November 21
Problem Set 12 due Tuesday December 5 (with automatic extension until anytime before final exam)